Ideal MHD ballooning instability and scaling law for confinement

The confinement time for an Ohmically heated, low-β tokamak is well described by the scaling law τ ∝ n. This implies that β should increase linearly with additional auxiliary heating power. In fact, the increase is much slower, and confinement deteriorates with increasing auxiliary heating. The possibility that this deterioration is due to the localized onset of MHD ballooning instabilities, with confinement elsewhere continuing to follow the law established for Ohmic discharges, is examined. It is found that the overall effect of the ballooning instability is indeed gradual and the resultant confinement time corresponds to a scaling law in good agreement with that reported for auxiliary-heated tokamaks.